The Government managed to get this year's €3.1bn payment for the wind-up of the bank postponed before the fiscal treaty referendum.
But it now faces paying another €3.1bn installment of the debt IOU – which is known as a promissory note – on March 31.
It is under increasing pressure to reach a deal on this because the gradual repayment of the €31bn Anglo debt is adding €1.9bn to the State's massive interest bill next year.
Mr Rabbitte made it clear that there was no intention of paying the next €3.1bn installment of the Anglo IOUs by the March 31 deadline.
"We didn't pay the promissory note this year and as far as I'm concerned we're not going to pay it next year either," he said.
"It's as simple as that."
Mr Rabbitte's comments went further than any of his cabinet colleagues, who have spoken only about efforts to strike a deal on the debt.
The Department of Finance said last night that Mr Rabbitte's remarks were broadly in line with previous comments made by Finance Minister Michael Noonan, who also said the Government does not want to pay the €3.1bn tranche of Anglo debt.
Mr Rabbitte went a step further with his "can't pay/won't pay" remarks on RTE's 'The Week In Politics'.
"We can't pay. This was an IOU entered into by the previous government when the Anglo Irish Bank collapsed and the notion of us paying it next March doesn't arise," he said.
Mr Rabbitte acknowledged that the ECB was a "difficult institution" to bring around to stamping the deal, but he believed it would be done before March 31.
The Government is not seeking a write-off of the Anglo debt, but is hoping to stretch out the repayments over a much longer period to relieve the pressure on the national finances.
Mr Rabbitte's decision to step up the rhetoric was welcomed by government backbenchers, who are aware that paying another €3.1bn towards the cost of Anglo would be politically disastrous after last week's cost-cutting Budget.
Fine Gael chairman Charlie Flanagan said it was "absolutely essential" to get a favourable deal on the Anglo debt.
"The justified harsh reaction to the Budget is accentuated by the fact that most of the money saved will go to meet our promissory notes requirement. I find it hard to stomach," he said.
The repayment of the €3.1bn Anglo IOU is built into the figures for Budget 2013. However, the Department of Finance has emphasised that even without this, the €3.5bn in spending cuts and tax increases would still be needed to reduce the huge gap between current spending and income.
Labour chairman Colm Keaveney said a clear message had to be sent to Europe that an Anglo debt deal was a critical step towards economic recovery.
"We've honoured the debt of private banks and it's causing great strain," he said.